How do you simplify $i^247$ ?

Question

4838 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-19T19:09:21

A great trick to solving this type of problem is understanding that there are only 4 possible solution ...

Raising the imaginary number $i$ to a power can only result in 4 possible solutions :

$i^0=1$
$i^1=i$
$i^2=-1$
$i^3=-i$

Here's the trick ... divide the exponent by the number 4 and calculate the remainder. Then, use the remainder as the new exponent .

In this example, $247/4=61 " with remainder " 3$

Answer: $i^247=i^3=-i$

hope that helped

How do you simplify i^247i^247?